Since the publication of PNP's list of numbers for indexed crimes per city (Table 1), many people have been sharing it in social media to compare one city to another. I think this is wrong. One can only compare two things regarding a particular variable if you make other variables constant. There are four major variables:

Years of Observation. The data for one year may be different in the next year.

City Population. If the city has more inhabitants, then you should expect that more crime will occur there.

City Area. If the city has a large area with a low population density, then you should expect to be safer there within your neighborhood.

What we need is to compare one city to another using only one or two indices that would reflect the overall criminality in the city.

II. METHODOLOGY

A. Averaging by Year, Population, and Area1. Years of Observation
PNP says that their data is for CY 2010-2015. Jon Cabuenas of GMA News concluded that this must be for 5 years. This is also the same view of Mig Garcia in his Facebook post "What's wrong with PNP's Crime Index?", though he corrected this in the Part 1 of his report: Is Quezon City the most dangerous city in the Philippines? Part 1: A closer look at the data." In his Endnote, he wrote: "The PNP reports crime data on a yearly basis. Hence, "2010 to 2015" does not cover only five years, but six." This makes sense since CY refers to calendar year, which begins on January 1 and ends on December 31 of the year. Thus, CY 2010-2015 refers to CY 2010, 2011, 2012, 2013, 2014, and 2015--a total of 6 years. So to get the values per year, I divided the numbers in PNP's crime index by 6 and not by 5.

2. City Population

For the same crime category, we can compare each city by computing what percentage of this crime occurred with respect to the city's population.But since the numbers are too small if we use per 100 people, we have to use larger population standards. So what I propose is to use the 2010 population sizes of each city, just as Mig Garcia had done.But instead of the 100,000 people standard that he proposed, I shall propose the 1,000,0000 people standard, since the City of Manila, Davao City, and Quezon City already have more than one million people each. The crime numbers per million people would then be large enough with comparable significant digits to that of the PNP data, so that we can dispense with showing numbers after the decimal points.

3. City Area

For the same population size, cities covering larger land areas would have lesser crime density per square kilometer than cities with smaller land areas.So we propose an index that measures for each crime category the total number of occurrences per year per square kilometer. This is similar to the comment of Bob Couttie to Mig Garcia, which Mig promised to do in the part 3 of his work. Mig Garcia has finished his plots in the Part 3 of his report: Is Davao City still the murder capital of the Philippines? Part 3: Gotham and the Myth. So essentially, Mig did not get the crime density per square kilometers: he only correlated the number of crimes reported with population density. So his work is different from what I'll do in this paper.

B. Crime Unit Analysis

1. Crime Unit

PNP has 6 categories for indexed crimes: murder, homicide, physical injury, robbery, theft, and carnapping. How do we compare things without a common unit of measurement? Mig Garcia proposed a simple weighting method after controlling the population by treating all crimes as equal and even all ranks as equal:

"There are two approaches to address this problem, but we will only do one here. The more complex approach is to provide a weighting criteria. For example, consider allocating a hundred percent to each of the six crime categories based on a criteria like the gravity of the crime or the amount of surveillance needed to catch suspected criminals. But because I do not have any prior knowledge about these weights, then we resort to an easier approach in normalizing data: averaging category ranks.

The procedure is fiendishly simple: for each crime category, rank each city based on their average yearly reported crime and add or take the average for all these crime categories. From there, rank the scores to determine the final ranking of the cities." -- Mig Garcia

In this paper, I shall take the more complex approach, which Mig Garcia proposed but has not attempted because it is more difficult, for it touches on philosophical and even theological issues. Even Christ said that humans are more valuable than animals, food, or clothing:

"Therefore I tell you, do not worry about your life, what you will eat [or drink], or about your body, what you will wear. Is not life more than food and the body more than clothing? 26Look at the birds in the sky; they do not sow or reap, they gather nothing into barns, yet your heavenly Father feeds them. Are not you more important than they?" (Mt 6:25-26)

From purely economic standpoint, we may be able to compare these different crimes through the peso equivalent of the good that they deprived. As a unit of measurement we shall use the average Filipino family's annual income for year 2012 of about Php 235,000 or roughly Php 20,000 per month, as given by Philippine Statistics Authority. We shall use this annual income as one crime index unit.b. Murder and Homicide (15 crime units)

Though they both result in the killing of a person, murder is distinguished from homicide by the intention to kill the person prior to the act. From the economic point of view, both murder and homicide are the same since the killing deprives the family of a source of income that the person can provide.
To compute how many crime index units is murder or homicide, we first note that the median age of Filipinos is 23.2 years old (CIA Factbook). Let's make that 23 years and make this the age a person is killed. Since the Philippine population decreases linearly to about zero at 83 years old, we can see that the potential inflation-adjusted income of that person who was killed also decreases along the way, because he may not survive up to venerable age: he may get killed while driving his new car at the age of 30, die of a heart attack at age 50 after watching a MMA fight, or get a bad fall at age 70. So his potential income is approximately half of his current salary per year multiplied by 83 - 23 = 60 years. This is equivalent to his present income, but he lives only about half the time at 30 years.

If we assume that the household has only two income earners, the husband and wife, and that children will someday form their own families, then each person murdered should have an earning potential of approximately half the average annual income of the average Filipino household. Thus, if we define one crime unit by the average income of the average Filipino household, then the the number of crime units for murder or homicide should be 30 x 0.5 = 15.

Physical injury can result to hospitalization, which we may estimate to about one month income of the household.So we simply divide one crime unit by 12.

Theft and robbery may also be estimated to about one month income of the household or about Php 20,000. Hot items would be cellphones and computers which may range from 10,000 to Php 50,000 or more.

d. Carnapping (2.5 Crime Units)

If we peg the price of the average car to about Php 500,000, and include the costs of ownership spread over 5 years, you get about Php 244,000, which is roughly equal to the average income of a Filipino household of Php 235,000:

If you add all the annual cost factors together including the
depreciation, spread in five years, that will result in the car’s
five-year cost of ownership. Say for example you have a P500,000 car
acquired through a bank loan that is payable in five years, your annual
expenses include: P101,832 in amortization; P66,000 in fuel; P15,000 in
insurance premiums; allot P10,000 for preventive maintenance; P5,000 for
consumables and repairs; and P47,000 in depreciation, the amount of
P244,832 will be the car’s actual cost of ownership every year. (Anjo Perez, The Manila Times)

If we assume that old and new cars are equally probable in being carnapped and they all have roughly the same number on the road, then the average age of the car would be 2.5 years, which is about 2.5 times the average income of a Filipino household. Thus, when the car was carnapped, the amount of money that the family invested on the car would be gone equal to 2.5 crime units.

e. Crime Index of the City

The city's overall crime index per year may be computed in terms of crime units using the weighting system we described earlier. That is,

Notice that human life is cheap: it's roughly equivalent to 2.5 cars. That's why some people are willing to kill for a car.

After computing the city's crime index, we can then compute three things:

Crime index per population per year.

Crime index per square kilometers of the city's land area

Crime index radius in kilometers

To get the crime index radius, we first divide the total land area of the city by the city's overall crime index, to get the number of square kilometers per crime index unit per year, which we may interpret as the size of the neighborhood where the total crime amounted to the average annual income of the Filipino household of roughly Php 235,000. We then find the circle with the same area as this neighborhood and compute the radius of this circle in kilometers. The bigger this radius is, the safer is the city.

We shall divide both the crime index per population per year and the crime index per square kilometers per year with their corresponding highest values across cities. The city with the highest normalized crime index values will have a value of 1, meaning dangerous; those with normalized crime index values close to zero are safe. After normalizing these crime index values, we shall rank the cities from 1 to 15, with 1 being the most-crime infested (dangerous) and 15 as the safest.

To provide a comparison of cities for different crime categories, we shall also divide the crime index of each city for a each crime category by those of the cities with the highest numbers for each respective crime category. Just like before, the city with the highest normalized crime index values for a particular crime category will have a
value of 1, meaning dangerous; those with normalized crime index values
close to zero are safe.

We shall not anymore normalize the crime index radius and rank different cities with it, since this quantity is not independent: it is inversely proportional to the square root of the crime index per square kilometers.

C. RESULTS AND DISCUSSION

1. PNP Data on Indexed Crimes for CY 2010-2015

Table 2 is a reordering of the PNP data on indexed crimes arranged alphabetically according to the names of each city. There's are two mistakes in the PNP table: the Theft column should total 188,959 and not 188958. Also, the row for the City of Manila should total 53,026 and not 54,689. The latter was also noted by Mig Garcia.

In Figures 4 to 9, I divided the number of of different crime categories--murder, homicide, physical injury, robbery, theft, and carnapping--in PNP data for CY 2010-2015 by 6 to get their respective occurrenceper year. I divided the result by the population of the city, and multiplied the fractional result by 1,000,000 to get the occurrence of the crime per 1,000,000 persons per year. I also divided the number of murder crimes per year by the total land area of the city to get the crime occurrence per square kilometer per year. This crime area density I then used to compute for the crime index radius in kilometers per year.

To help the reader follow the computations, I listed the cities and their populations and land areas in the columns prior to those of the PNP data and the population ratio and area density.

Table 5. Physical injury crimes per year per city population and city area

Table 6. Robbery crimes per year per city population and city area

Table 7. Theft crimes per year per city population and city area

Table 8. Murders crimes per year per city population and city area

3. Crime Indices of Each City Per Year, Per Population, and Per sq. km

Table 9 summarizes the average crime occurrences per year for different crime categories for different cities. To compute the crime index per year, the following weighting system was employed: murder (15), homicide (15), physical injury (1/12), robbery (1/12), theft (1/12), and carnapping (2.5). The numbers are then added to obtain the crime index per year.

Table 10presents the computation for the crime index of each city per year as a fraction of the population in terms of 1,000,000 population standard. Table 11 is a similar computation, except that the divisor is not the total population of each city, but the city's total land area.Table 12 lists the corresponding radii of different crimes given their crime area densities in Table 11.

Table 10. Average crime occurrence per city per year per 1,000,000 persons.

Table 11. Average crime occurrence per city per year per square kilometer

Table 12. Average crime occurrence radius per city per year.

4. Normalized Crime Indices of Each City Per Year, Per Population, and Per sq. km

Table 13 presents the crime occurrence per 1,000,000 person per year normalized with respect to the highest value of each crime category. The numbers in gray background are those which exceed half of the highest value of 1: these cities are dangerous for the particular crime categories.

Tables 15 and 16 summarizes the ranking of each each city according to its crime indices per population and per sq. km. These indices were normalized with respect to the highest values per category, so that those who get a normalized index of 0 are safe, while those who get 1 are dangerous.

Table 13. Crime occurrence per city per year normalized with respect to the highest value per crime category

Table 14. Crime occurrence per city per year per sq. km normalized with respect to the highest value per crime category

Table 15. Crime index per city per year per 1,000,000 persons and per sq.
km. The values were normalized with respect to the highest value per
category and ranked accordingly.

Table 16. Crime index rankings of Philippine cities

D. CONCLUSIONS AND RECOMMENDATIONS

PNP has provided a list of numbers for indexed crimes per city. But these numbers alone are insufficient to compare one city from another because cities vary by population and land area. Also, different crimes have different gravity, e.g. murder is much graver than theft. What is needed then is to have a single number to compare one city from another, assuming they have the same population and land area, with different crime categories given different weights according to the gravity of the deed.

In this blog post we proposed a crime index with a unit value equal to the average annual income of a Filipino household of 4.6 members. We then gave weights to different crime categories according to the cost of the goods they deprived their victims. Murder and homicide we gave a weight of 15. Physical injury, robbery, and theft, we gave a weight of 1/12. And lastly, for carnapping, we gave a weight of 2.5. We multiplied the value for each crime by its weight, then added up the result to get the crime index for each city.

After computing the crime index of each city, we divided it by the city population and multiplied the result by one million to obtain a crime index per one million population. We also divided the crime index of the city by the city's total land area to compute the crime index per sq. km. We normalized these ratios with respect to the highest number per category. We then obtained the average of these two ratios to obtain the crime index of each city. We used this to rank each city's crime level.

If we rank the crime level of each city as percentage of population, Cebu City and Cagayan de Oro City would rank 1 and 2, while Mandaue City and Makati City would rank 14 and 15. On the other hand, if we rank the crime level of each city per sq. km of land area, Manila and Makati would rank 1 and 2, while Davao and Iligan would rank 14 and 15. Overall, Manila and Cebu ranks 1 and 2 in crime level, while Bacolod and Naga rank 14 and 15.

By defining the level of criminality in terms of the Filipino household's average annual income, we can see immediately the effect of crime on the Filipino family. Murder and homicide deprives the family of present and future income generators. Physical injury drains the family income in hospitalization costs. And theft, robbery, and carnapping deprives the family of the goods which were purchased from the family income. The Philippine National Police may wish to adopt the crime index formula presented here
or modify it in light on more data regarding the actual cost of different crimes to the Filipino family.

This May 2016 elections, we should vote not just someone who will stop crime in the cities, but who shall also promote the welfare of the family as well, for crime is just a symptom of broken families--of families who failed to rear their children into the world as God-fearing citizens. You shall not kill. You shall not steal. You shall not covet your neighbor's goods. These are the Fifth, Seventh, and Tenth Commandments which pertain to crime. What was not included in this study are those crimes involving the Fourth, Sixth, and Ninth Commandments which pertain to marriage and family: "Honor your father and mother. You shall not commit adultery. You shall not covet your neighbor's goods." If the data on these are available, we shall extend the study to cover these.

We need to vote for politicians who are pro-life and pro-family, not just those running for presidency and vice-presidency, but also those running for senators, congressmen, governors, mayors, and all the way down. We also need to vote for party-lists. So if you have not yet made up your mind what partylist to vote for this May 2016 elections, I strongly urge you to consider voting for Ang ProLife partylist #109. Ang Prolife Partylist has a strong pro-life and pro-family advocacy: the partylist is against same-sex marriage, death penalty, divorce, contraception, and sex education because these destroy the Filipino family. Ang ProLife Partylist is also supported by Filipinos for Life, which has a deep pool of professionals and technical experts from diverse fields--nursing, medicine, business, law, media, physics, engineering, manufacturing, philosophy, theology, etc.--all working for the culture of life and the welfare of the family in the country. So this May 2016, please remember your family and vote Ang Prolife Partylist #109.

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